UNIVERSITI PUTRA MALAYSIA

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1 UNIVERSITI PUTRA MALAYSIA THEORY AND SIMULATION OF THE ONSETS OF CONVECTION INDUCED BY LIQUID DIFFUSION IN LIQUID AND INCIPIENT INSTABILITY CAUSED BY LIQUID FLOW PARTICLE BED SIEW FONG WAH. FK

2 THEORY AND SIMULATION OF THE ONSETS OF CONVECTION INDUCED BY LIQUID DIFFUSION IN LIQUID AND INCIPIENT INSTABILITY CAUSED BY LIQUID now IN PARTICLE BED BY SIEW FONG WAH Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in Fulfilment of the Requirements for the Degree of Master of Science March 2006

3 To Dad and Mom

4 Abstract of thesis presented to the Senate of Universiti Putra Malaysia in fulfilment of the requirement for the degree of Master of Science THEORY AND SIMULATION OF THE ONSETS OF CONVECTION INDUCED BY LIQUID DIFFUSION IN LIQUID AND INCIPIENT INSTABILITY CAUSED BY LIQUID now IN PARTICLE BED SIEW FONG WAH March 2006 Chairman: Faculty: Associate Professor Thomas Choong Shean Yaw, PhD Engineering The theory of transient instability of gas in aqueous liquid proposed by Tan and Thorpe (1999) was extended to study the onset of convection induced by liquid diffision in liquid. 2D time-dependent simulations were conducted using a CFD package - FLUENT to verify the analysis of transient instability. The onset of buoyancy convection induced by liquid mass difhsion was simulated for water diffused into 1-butanol, ethyl acetate and 2-butanone at different temperatures. The formation and the development of the convection plumes were successfully simulated. The transient liquid diffusion simulation was verified using Fick's Law. The average simulated transient Rayleigh number was found to be 1315, which was close to 1404, i.e. the average value of critical Rayleigh number of 1100 and 1708 for boundary conditions with fiee-solid and solid-solid surfaces. The simulated onset time, the critical difhsion depth and the size of the plumes were found to agree well with values predicted by theory.

5 By recognizing that the mass transfer effect is very much smaller compared to the effect of momentum difhsion in causing the incipient instability in particle bed, the transient critical Rayleigh number proposed by Tan (2004) was re-defined based on momentum difhsion. The time-dependent simulations for incipient instability caused by liquid flow in particle bed were performed for different particle sizes, flow rates and initial bed heights. The CFD simulations were verified by the variation of particle bed height with superficial velocity. The onset time of incipient instability could be determined by the series contours of volume fraction, velocity vectors and maximum velocity. The simulated critical Rayleigh numbers based on the momentum diffusion were found to be inconsistent. A modified critical Rayleigh number was proposed by incorporating a factor of z,lh to the critical Rayleigh number. The simulated modified critical Rayleigh number was found to be almost constant, Ra,' = 16.8, which was very close to the theoretical value of 17.7 for buoyancy instability for porous media.

6 "..I-- Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi keperluan untuk ijazah Master Sains TEORI DAN SIMULASI UNTUK PERMULAAN PEROLAKAN DISEBABKAN OLEH RESAPAN CECAIR DALAM CECAIR DAN INSIPIEN KETIDAKSTABILAN DISEBABKAN OLEH ALIRAN CECAIR DALAM LAPISAN BUTIRAN Oleh SIEW FONd WAH Mac 2006 Pengerusi: Profesor Madya Thomas Choong Shean Yaw, PhD Faculti: Kej uruteraan CC-- Teori transien ketidakstabilan gas dalam cecair akueus yang dicadang oleh Tan and Thorpe (1999) disambung untuk mengkaji permulaan perolakan yang disebabkan oleh resapan cecair dalam cecair. Simulasi 2D bergantung masa telah dilakukan dengan menggunakan pakej CFD - FLUENT untuk mengesahkan analisa ketidakstabilan transien. Permulaan perolakan pengapungan yang disebabkan oleh resapan jisim cecair telah disimulasi untuk resapan air ke dalam 1-butanol, etil asetat dan 2-butanol pada suhu yang berlainan. Pembentukan dan perkembangan plume perolakan yang disebabkan oleh resapan jisim transien apabila cecair meresap ke dalam cacair berlainan telah disimulasi dengan berjaya. Simulasi resapan ceciar transien disahkan dengan menggunakan Hukum Fick. Purata nombor Rayleigh transien yang disimulasikan adalah 1315, hampir dengan 1404, iaitu nilai purata nombor Rayleigh kritikal 1100 and 1708 untuk keadaan sempadan dengan permukaan bebas-pepejal dan pepejal-pepejal. Masa permulaan, kedalaman resapan kritikal dan saiz plume yang disimulasi didapati bersetuju dengan nilai yang diramal daripada teori.

7 Dengan pengetahuan bahawa kesan pemindahan jisim adalah sangat kecil berbanding dengan kesan resapan momentum dalam menyebabkan insipien ketidakstabilan dalam lapisan butiran, nombor Rayleigh kritikal transien yang dicadangkan oleh Tan (2004) didefinasikan semula berdasarkan resapan momentum. Simulasi bergantung masa untuk insipien ketidakstabilan yang disebabkan oleh aliran cecair dalam lapisan butiran dilakukan untuk pelbagai saiz butiran, kadar aliran dan ketinggian lapisan butiran awal. Simulasi CFD disahkan dengan perubahan ketinggian lapisan butiran dengan halaju superfisial. Masa permulaan insipien ketidakstabilan dapat ditentukan dengan siri kontur pecahan isipadu, vektor halaju dan halaju maksimum. Nombor Rayleigh kritikal berdasarkan resapan momentum yang disimulasi didapati adalah tidak tetap. Nombor Rayleigh kritikal yang diubahsuai dicadang dengan menggabungkan faktor zjh kepada nombor Rayleigh kritikal. Nombor Rayleigh kritikal diubahsuai yang disimulasi didapati adalah tetap, Ra,' = 16.8, sangat hampir dengan nilai teori 17.7 untuk ketidakstabilan pengapungan untuk poros media.

8 ACKNOWLEDGEMENT It is with profound gratitude that I would like to thank my esteemed supervisor and mentor, Associate Professor Dr. Thomas Choong Shean Yaw and Professor Ir. Dr. Tan Ka Kheng, for their constructive input, thoughtful comments, brilliant guidance and patient supervision of my work. Heartfelt thanks towards Mr. Tan Yee Wan who had tirelessly taught me to master the simulation package, Mr. Sreenivas, support and consulting engineer in FLUENT (India), and Mr. Look Kar Yang for their valuable suggestions and advices in conducting my simulation. Also my thanks to Dr. Siti Aslina, Dr. Mohamad Arnran, Dr. Tay and Dr. Ling for their generous advices in helping me to materialize my theses. Lastly, I would like to thank my friends for their encouragement throughout the course of this project.

9 I certify that an Examination Committee has met on 23* March 2006 to conduct the final examination of Siew Fong Wah on his Master of Science thesis entitled "Theory and Simulation of the Onsets of Convection Induced by Liquid Diffusion in Liquid and Incipient Instability Caused by Liquid Flow in Particle Bed" in accordance with Universiti Pertanian Malaysia (Higher Degree) Act 1980 and Universiti Pertanian Malaysia (Higher Degree) Regulations The Committee recommends that the candidate be awarded the relevant degree. Members of the Examination Committee are as follows: Suraya Abdul Rashid, PhD Lecturer Faculty of Engineering Universiti Putra Malaysia (Chairman) Luqman Chuah b. Abdullah, PhD Associate Professor Faculty of Engineering Universiti Putra Malaysia (Internal Examiner) Mohamad Amran Mohd. Salleh, PhD Lecturer Faculty of Engineering Universiti Putra Malaysia (Internal Examiner) Wang Chi Hwa, PhD Associate Professor Faculty of Engineering National University of Singapore (External Examiner) School of Graduate Studies Universiti Putra Malaysia Date: I 1 JUC 2006 vii

10 This thesis submitted to the Senate of Universiti Putra Malaysia and has been accepted as fulfilment of the requirement for the degree of Master of Science. The members of the Supervisory Committee are as follows: Thomas Choong Shean Yaw, PhD Associate Professor Faculty of Engineering Universiti Putra Malaysia (Chairman) Siti Aslina Hussain, PhD Lecturer Faculty of Engineering Universiti Putra Malaysia (Member) AINI IDERIS, PhD ProfessorIDean School of Graduate Studies Universiti Putra Malaysia Date: 10 AUG 2006

11 DECLARATION I hereby declare that the thesis is based on my original work except for quotations and citations which have been duly acknowledged. I also declare that it has not been previously or concurrently submitted for any other degree at UPM or other institutions. Date: L h06

12 TABLE OF CONTENTS DEDICATION ABSTRACT ABSTRAK ACKNOWLEDGEMENT APPROVAL DECLARATION LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONSINOMENCLATURE Page. 11 iii v vii viii X xiv xv xvii CHAPTER INTRODUCTION LITERATURE REVIEW 2.1 Introduction 2.2 Theory of Transient Instabilities and Convection 2.3 Experimental Studies of Convection Caused by Density Gradient 2.4 Instabilities in Fluidized Bed 2.5 Flow Pattern in Liquid Fluidized Bed 2.6 Overview DEVELOPMENT OF THE TRANSIENT INSTABILITY THEORY 3.1 Introduction 3.2 The Onset of Buoyancy Convection Induced by Transient Liquid Diffusion in Liquid Fixed Surface Concentration (FSC) Boundary Condition Determination of Saturated Concentration and Molar Density Coefficient of Liquid in Liquid 3.3 The Onset of Incipient Instability Caused by Liquid flow in Particle Bed Minimum Fluidization Velocity 3.4 Overview MATERIALS AND METHODOLOGY 4.1 Computational Fluid Dynamics (CFD) Simulations 4.2 Overall Solution Algorithm 4.3 Simulation of Species Transport Model for Buoyancy Convection Induced by Transient Mass Diffusion in Liquid Conservation of Mass, Heat and Momentum Transfer Used in Species Transport Model

13 4.4 Simulation of Eulerian Multiphase Model for Incipient Fluidization Caused by Liquid Flow in Particle Bed Conservation Equations in Eulerian Multiphase Model Fluid-Solid Exchange Coefficient for Fluidized Bed 4.5 Numerical Considerations and Constrains in CFD Simulation 4.6 Simulations Setup Determination of Physical Properties for the Onset of Convection caused by Liquid Diffision in Liquid Simulation Setup for the Onset of Convection Caused by Liquid Diffusion in Liquid Simulation Setup for the Onset of Incipient Fluidization Caused by Liquid Flow in Particle Bed Overview RESULTS AND DISCUSSIONS Introduction Simulations of the Onset of Buoyancy Convection Caused by Liquid Difhsion in Liquid Transient Rayleigh Number for Onset of Convection Critical Time for the Onset of Convection Evolution of the Convection Plumes Critical Penetration Depths and Critical Wavelength Maximum Velocity of Convection Mass Flux and Mass Transfer Coefficient Simulations of the Onset of Incipient Fluidization Caused by Liquid Flow in Particle Bed Simulated Flow Behaviour and the Onset of Incipient Fluidization Caused by Liquid Flow in Particle Bed Maximum Velocity for Liquid Flow through Particle Bed Critical Rayleigh Number and Onset Time of Incipient Instability Overview CONCLUSIONS RECOMMENDATIONS xii

14 REFERENCES APPENDICES BIODATA OF THE AUTHOR Xlll...

15 LIST OF TABLES Table Page Summary of the critical Rayleigh number equations derived Settings of the simulation cases for liquid diffusion in liquid Simulation settings for different cases Simulated transient Rayleigh Number and the onset time of 5.4 convection for top-down liquid difhsion Comparison of the predicted and simulated critical diffusion 5.10 depth when water di&ses into other liquids Comparison of the predicted and simulated critical wavelength when water diffuses into other liquids Simulated and predicted onset times and critical Rayleigh 5.27 numbers of incipient instability xiv

16 LIST OF FIGURES Figure Page The three regimes of onset motion for sulphur dioxide-water 2.7 system observed by Blair and Quinn (1968) 2.2 Typical elements of flow patterns at the gas-liquid intefiace 2.9 (Okhotsimskii and Hozowa, 1998) 2.3 Flow visualization during carbon dioxide absorption into 2.10 ethylbenzene and isobutanol by Okhotsimskii and Hozowa (1998) 2.4 Growth of a two-dimensional perturbation of the uniform state 2.14 for 1-mm glass beads fluidized by water (Glasser et al., 1997) 3.1 Development of the concentration gradient induced by top-down 3.3 transient mass diffusion Flow through particle bed Overview of the segregated solution method Comparison of the grid size effect on the concentration profile The settings of computational domain for the onset of convection 4.14 when liquid difhse into liquid 4.4 The setting of computational domain for the onset of incipient 4.17 instability caused by liquid flow in particle bed 5.1 The onset of buoyancy convection caused by diffusion of water 5.2 in 1-butanol at 10 s Critical transient Rayleigh number for top-down liquid difision 5.3 Comparison of the simulated and predicted onset times of 5.5 convection for water diffusing into other liquids Series contours of mass fiactions and velocity vectors of water 5.9 for water diffising into ethyl acetate at 25OC Comparison of the simulated and predicted critical difision 5.10 depth when water diffising into other liquids Comparison of the simulated and predicted critical wavelength when water diffusing into other liquids

17 Maximum velocity history for water diflksing into 1-butanol Maximum velocity history for water difising into ethyl acetate Maximum velocity history for water diflbsing into 2-butanone Comparison of the simulated and predicted mass transfer for case 5.14 A with onset time of convection equal to 10 s Comparison of the simulated and predicted mass transfer 5.15 coefficient for case A with onset time of convection equal to 10 s Height of the particle bed at various superficial velocities No fluidization observed when superficial velocity is 0.05 mls or Umf Fluidization occurred when superficial velocity is ds, Umf Contours of volume fraction of dimethyl phthalate when 5.19 superficial velocity is rnls or - 4 UM Series contours of volume fraction of dimethyl phthalate for case Series of velocity vectors of dimethyl phthalate for case 4 Maximum liquid velocity at the particle bed inlet at tc = 0.9 s 5.23 (case 3) Maximum liquid velocity at the particle bed inlet with tc = 0.6 s 5.24 (case 4) Modified critical Rayleigh numbers vs. onset times Modified critical Rayleigh numbers vs. onset times Comparison of the simulated and predicted onset times of 5.27 incipient instability

18 LIST OF ABBREVIATIONSINOMENCLATURE center coefficient influence coefficients for the neighboring cells dimensionless critical wavenumber total area of the cross section of the bed column, m2 bulk concentration or saturated concentration of solute, kmol/m3 or kg/m3 initial concentration of solute, kmol/m3 or kg/m3 concentration, kmol/m3 or kg/m3 drag function bed diameter, m particle diameter, m difhsivity of mass, m2/s total energy, J external body force, N lift force, N virtual mass force, N gravitational force, m/s2 heat transfer coefficient, w /m2.~ height of the particle bed, m height of simulation chamber, mm mass transfer, kg/m2 constant mass flux, kg/m2.s thermal conductivity, W/m C effective conductivity, W1m.K solid-fluid exchange coefficient permeability, m2 molality, mollkg constant heat flux, w/m2 molecular weight of a component, kg/kmol pressure drop across the bed, Pa residual xvii

19 interaction force between phases, N time, s time step interstitial velocity, m/s superficial velocity of the mass flow, m/s interstitial velocity, m/s minimum fluidization velocity, m/s molar volume, m3/kmol partial molar volume, m3/kmol apparent molar volume, m3/kmol weight of the solids in the bed, kg width of simulation chamber, mm mass fraction of component, kglkg mole fraction of component, kmol/kmol effective distance of the mass diffusion, m Greek Symbols density, kg/m3 exchange coefficient molar density coefficient, kglkmol thermal expansion, 1/K thermal diasivity, m2/s particulate relaxation time, s porosity qth phase stress-strain, Pa shape factor of particle or sphericity terminal velocity correlation for the solid particle tortuosity dynamic viscosity, kglms difisivity of momentum, kinematic viscosity, = p /p, m2/s wavelength, m xvi i I

20 Abbreviations LSA FSC Linear Stability Analysis Fixed Surface Concentration CMF Constant Mass Flux Bi Gr Ra Re Sc Biot number Grashof number Rayleigh number Reynolds number Schmidt number Subscripts c c f n i o P s v w eff max critical solid particle bed fluid 1 -butan01 interfaci a1 initial state particle solution of solute and solvent voids water effective maximum xi,

21 CHAPTER 1 INTRODUCTION Mass transfer may produce density gradient that in turn causes free convection. As an example, imagine that a crystal of salt is held just under the surface of initially stagnant water. The salt dissolves and difises away from the crystal, producing a solution near the crystal that is denser than the water itself This solution flows downward, and the resulting flow increases the rate of mass transfer. Thus, mass transfer and flow couple to accelerate dissolution. The natural convection in a binary gas-liquid system (Okhotsimskii and Hozowa, 1998; Blair and Quinn, 1969) and Maragoni-unstable interfacial turbulence at liquidliquid interface (Sternling and Scriven, 1959; Orell and Westwater, 1962; Nakaike et al., 1969) have been extensively studied. The transient instability theory of gas difhsion in liquid that leads to the onset of buoyancy convection has been reported by Tan and Thorpe (1996, 1999). However, the case of a Rayleigh-unstable binary liquid system in which the density-driven plume convection happens has attracted much less attention (Berg and Morig, 1969). A new transient Rayleigh number is needed to study the onset of convection induced by liquid diffusion in liquid. The density gradient developed by transient liquid mass diflision of a solute in a solvent may contribute to the convection accompanying the mass transfer.

22 The knowledge of natural convection induced by diffusing liquid into a stagnant liquid is of considerable interest because of its importance in the study of mass transfer of liquid solute in solvent for biological and pharmaceutical use, dispersion of emuent in treatment plants and lakes, and other engineering applications. Convection causes more liquid to be dissolved in the solution compared to diffusion. Fluidization is a two-phase contact process which relies on keeping up the grains of solid substance in suspension state in the flux flowing up with appropriate velocity. The fluidization plays an essential role in many engineering processes because intensive mixing of phases is conductive to all sorts of diffusion phenomena, such as: intensive exchange of mass and heat, generation of uniform field of temperatures, etc. The linear stability analysis (LSA) was first employed by Jackson (1963) to study the onset of incipient instability by assuming a convection mechanism. The inertia force of the particle imparted by average fluid velocity was found to contribute to the instability. Past researches considered the increase of voidage as an indicator of the onset of fluidization, although the expansion of voidage is in fact a consequence of fluidization of the bed. The main cause of incipient fluidization is the momentum of the high incoming flux that overcomes the buoyancy force of the solid particles. Moreover, the incipient

23 instability is preceded by the flowing of the liquid into the interstices of the particle bed with a mass flux or superficial velocity exceeding the minimum fluidization velocity, U@ Therefore the first abrupt increase of flow velocity should be the indicator of the onset of incipient fluidization when the localized saturation of the interstices is suficient to lift the particles. The onset of incipient fluidization caused by liquid flow in particle bed is coupled with the immense change of mass fraction of the liquid in the region close to the flow inlet. The objectives of this work are to study the onset of convection caused by liquid difision in liquid and the onset of incipient instability caused by liquid flow in particle bed. A critical Rayleigh number will be derived for the prediction of the onset of buoyancy convection when water diffuses into various partially miscible organic liquids at different temperatures. For the onset of incipient instability of liquid flow in particle, a critical Rayleigh number based on momentum diffbsion will be derived. The derivation performed in this study follow closely the principle of transient instability theories advanced by Tan and Thorpe (1996 and 1999) and Tan (2004). Two-dimensional time-dependent simulations will be conducted to verify the principles of transient instability. The onset of buoyancy convection induced by liquid mass diasion and the mechanism of incipient instability in a particle bed will be simulated using a CFD package, FLUENT. Parameters such as the onset time of

24 instability, critical difision depth, size of the plume and critical Rayleigh number will be obtained from simulations. This study predicts the particular mass transfer parameters for liquid difision in liquid as well as liquid flow in particle bed without conducting the real experiments. These experiments are hardly to be camed out as advanced technology and equipments are required. The simulated design of experiment in this research may shed some light for the experiment models.

25 PERPUSTAKAAN SULTAN ABDUL SAMAO UNNERSlTl PUTRA MALAYSIA CHAPTER 2 LITERATURE REVIEW 2.1 Introduction The theory of transient convection and instabilities will first be reviewed. This is followed by the discussion of the experimental studies of convective instability induced by adverse density gradient. The typical convection patterns are presented. Finally, discussions on the instability and flow pattern in liquid fluidized bed are given. 2.2 Theory of Transient Convection and Instabilities Lord Rayleigh (1916) derived a criterion for the onset of buoyancy convection in a fluid layer bounded by two free surfaces based on an adverse linear temperature gradient typical of steady-state heat transport; the stability criterion is rearranged later to become the well-known Rayleigh number, where g is the gravitational acceleration, #I is the thermal expansion, d is the depth of fluid layer, AT is the temperature difference of two surfaces, v is the kinematic viscosity and K is the thermal diffisivity. However, natural convection is induced by a time-dependent and non-linear temperature profile. Several definitions of time-dependent Rayleigh number were suggested by Howard (1964) and Davenport and King (1972), but none of them has